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Someone called Hammad Rana has created the stub Surreal geometry and the more substantial (but… odd) Surreal space. The latter claims to look at vector spaces over the surreal numbers and relate them to other things.
Thanks for the heads-up. I can’t tell immediately whether there is anything to be worried about; the writing is idiosyncratic, but not obviously wrong (to me), and it at least cites an arxiv paper by someone who isn’t Hammad Rana. What do you think?
I don’t know about the ’genetic’ stuff, but I don’t think $Vect_\mathbb{R}$ is a subcategory of $Vect_\mathbb{S}$. That’s not how modules work.
Statements like these (from various parts of the page) don’t give me confidence
The sheaf cohomology on a surreal space is equivalent to a motivic cohomology of real algebraic cycles
we can say that for a drawn line of surreal numbers we have that it is in a sense a projective line
A surreal space is a topos over the reals.
At one point the author says that
Surreal space (denoted as $\mathbf{S}^n$) can be seen as a topologically enriched category of a real space $\mathbb{R}^m$
and then claims that $Sur$ (this category) is a vector space over the reals and later says
This connection leads us to seeing that the asymptotic collection of real-valued functions is contained within $obj(Sur)$
It’s all rather strange, I don’t know what to make of it.
To me it reads as “not even wrong”: the language in places (e.g., those pointed out by David) doesn’t make sense. I don’t think we should spend much time on this, or try to nurse such entries into proper shape. That hasn’t worked out too well in the past.
Okay, I didn’t read it carefully enough at first. Shall we just delete it then?
Yes, let’s clear the page and leave a message. Something like
Please don’t continue editing. If you insist on discussing your ideas here, you can do so on the nForum, where regulars can give feedback and guidance. But we suggest that you try to take this discussion to another, more suitable forum. The Steering Committee.
I agree with Urs’ suggestion.
Ok, I changed Surreal space and Surreal geometry to a version of Urs’s suggested message.
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